Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sbhypf | Unicode version |
Description: Introduce an explicit substitution into an implicit substitution hypothesis. See also csbhypf . (Contributed by Raph Levien, 10-Apr-2004.) |
Ref | Expression |
---|---|
sbhypf.1 | |
sbhypf.2 |
Ref | Expression |
---|---|
sbhypf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2715 | . . 3 | |
2 | eqeq1 2164 | . . 3 | |
3 | 1, 2 | ceqsexv 2751 | . 2 |
4 | nfs1v 1919 | . . . 4 | |
5 | sbhypf.1 | . . . 4 | |
6 | 4, 5 | nfbi 1569 | . . 3 |
7 | sbequ12 1751 | . . . . 5 | |
8 | 7 | bicomd 140 | . . . 4 |
9 | sbhypf.2 | . . . 4 | |
10 | 8, 9 | sylan9bb 458 | . . 3 |
11 | 6, 10 | exlimi 1574 | . 2 |
12 | 3, 11 | sylbir 134 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wnf 1440 wex 1472 wsb 1742 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1427 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-v 2714 |
This theorem is referenced by: mob2 2892 cbvmptf 4058 tfisi 4546 ralxpf 4732 rexxpf 4733 nn0ind-raph 9281 |
Copyright terms: Public domain | W3C validator |